Decentralized CFAR signal detection

The authors develop the theory of CA-CFAR (cell-averaging constant false-alarm rate) detection using multiple sensors and data fusion, where detection decisions are transmitted from each CA-CFAR detector to the data fusion center. The overall decision is obtained at the data fusion center based on some k out of n fusion rule. For a Swerling target model I embedded in white Gaussian noise of unknown level, the authors obtain the optimum threshold multipliers of the individual detectors. At the data fusion center, they derive an expression for the overall probability of detection while the overall probability of false alarm is maintained at the desired value for the given fusion rules. An example is presented showing numerical results     

OS-CFAR thresholding in decentralized radar systems

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization     

Data fusion of multiradar system by using genetic algorithm

Detection system with distributed sensors and data fusion. are increasingly being used by surveillance systems. There has been a great deal of theoretical study on decentralized detection networks composed of identical or non-identical sensors. To solve the resulting nonlinear system, exhaustive search and some crude approximations are adopted. However, those methods often cause either the system to be insensitive to some parameters or the suboptimal results. In this paper, a novel flexible genetic algorithm is investigated to obtain the optimal results on constant false alarm rate data fusion. Using this approach, all system parameters are directly coded in decimal chromosomes and they can be optimized simultaneously. The simulation results show that adopting the proposed approach, one can achieve better performances than the reported methods and results     

Decentralized detection over multiple-access channels

We study the decentralized detection problem in a general framework where arbitrary number of quantization levels at the local sensors are allowed, and transmission from the sensors to the fusion center is subject to both noise and interchannel interference. We treat both Bayesian and Neyman-Pearson approaches to the problem, and develop an iterative descent algorithm to design the optimal quantizers and fusion rule. Some numerical examples for both approaches are also presented     

Optimal Data Fusion in Multiple Sensor Detection Systems

There is an increasing interest in employing multiple sensors for surveillance and communications. Some of the motivating factors are reliability, survivability, increase in the number of targets under consideration, and increase in required coverage. Tenney and Sandell have recently treated the Bayesian detection problem with distributed sensors. They did not consider the design of data fusion algorithms. We present an optimum data fusion structure given the detectors. Individual decisions are weighted according to the reliability of the detector and then a threshold comparison is performed to obtain the global decision.     

Nonparametric rank detectors under K-distributed clutter in radar applications

This correspondence deals with a comparative analysis of parametric detectors versus rank ones for radar applications, under K-distributed clutter and nonfluctuating and Swerling II target models. We show that the locally optimum detectors (LODs) (optimum for very low signal-to-clutter ratio (SCR)) under K-distributed clutter are not practical detectors; on the contrary, asymptotically optimum detectors (optimum for high SCR) are the practical ones. The performance analysis of the parametric log-detector and the nonparametric (linear rank) detector is carried out for independent and identically distributed (IID) clutter samples, correlated clutter samples, and nonhomogeneous clutter samples. Some results of Monte Carlo simulations for detection probability (P/sub d/) versus SCR are presented in curves for different detector parameter values.     

Distributed CFAR detection in homogeneous and nonhomogeneousbackgrounds

The performance of distributed constant false alarm rate (CFAR) detection with data fusion both in homogeneous and nonhomogeneous Gaussian backgrounds is analyzed. The ordered statistics (OS) CFAR detectors are employed as local detectors. With a Swerling type I target model, in the homogeneous background, the global probability of detection for a given fixed global probability of false alarm is maximized by optimizing both the threshold multipliers and the order numbers of the local OS-CFAR detectors. In the nonhomogeneous background with multiple targets or clutter edges, the performance of the detection system is analyzed and its performance is compared with the performance of the distributed cell-averaging (CA) CFAR detection system     

The case for like-sensor predetection fusion

There has been a great deal of theoretical study into decentralized detection networks composed of similar (often identical), independent sensors, and this has produced a number of satisfying theoretical results. At this point it is perhaps worth asking whether or not there is a great deal of point to such study-certainly two sensors can provide twice the illumination of one, but what does this really translate to in terms of performance? We take as our metric the ground area covered with a specified Neyman-Pearson detection performance. To be fair, the comparison will be of a multisensor network to a single-sensor system where both have the same aggregate transmitter power. The situations examined are by no means exhaustive but are, we believe, representative. Is there a case? The answer, as might be expected, is “sometimes.” When the statistical situation is well behaved there is very little benefit to a fused system; however, when the environment is hostile the gains can be significant. We see, depending on the situation, gains from colocation, gains from separation, optimal gains from operation at a “fusion range,” and sometimes no gains at all     

Simple Procedures for Radar Detection Calculations

The literature of radar contains results of Rice, Marcum, Swerling, and Schwartz in several families of curves, which permit radar engineersto estimate the signal energy ratio required for a given level of detectionperformance. The variety of radar problems, however, makes itimpractical to construct curves for all combinations of radar and targetparameters. The concept of detector loss is used here to evaluate lossesattributable to integration and collapsing, with an accuracy of ±0.3 dBon steady targets. This is added to a separate fluctuation loss, modifiedfor diversity effects, to obtain results on all Swerling target modelsand also on partially correlated targets. The accuracy of the combinedlosses is ±0.5 dB for a wide range of detection and false-alarm probabilities.Starting from the basic single-sample detection curves, onlythree additional graphs are needed to find the energy ratio for givendetection performance in any of these cases. Examples are given whichshow the ease with which different radar options may be compared asto performance on an arbitrary type of target.     

Hypotheses Testing in a Distributed Environment

The problem of optimum detection with n decentralized sensors selecting among m possible signals is considered from the decision theory point of view. The loss function is defined in terms of the decisions made by each observer and the transmitted signal. Then the average of this loss function is minimized. This leads to sets of coupled inequalities in terms of the likelihood ratio of each observer and the decisions made at the other sensors. This determines the structure of the optimum decentralized detection for an arbitrary number of sensors and an arbitrary number of possible signals. These results are valuable in numerous situations that may arise in large-scale and distributed systems.     

Monopulse-radar tracking of swerling III-IV targets using multiple observations

This paper proposes a novel statistical prediction of monopulse errors (Levanon, 1988) for a radar Swerling III-IV target embedded in noise or noise jamming where multiple observations are available. First, the study of the maximum likelihood estimator (MLE) of the complex monopulse ratio for a Swerling III-IV target embedded in spatially white noise allows us to extend the use of the MLE practical approximate form introduced by Mosca (1969) for Swerling 0-I-II cases. Afterward, we derive analytical formulas for both the mean and variance of the MLE in approximate form conditioned by the usual detection step performed on the sum channel of a monopulse antenna. Last, we provide a comparison of target direction of arrival (DOA) estimation performance based on monopulse ratio estimation as a function of the Swerling model in the context of a multifunction radar.     

Explicit solutions for some simple decentralized detection problems

A decentralized detection problem is considered in which a number of identical sensors transmit a finite-valued function of their observations to a fusion center which makes a final decision on one of M alternative hypotheses. The authors consider the case in which the number of sensors is large, and they derive (asymptotically) optimal rules for determining the messages of the sensors when the observations are generated from a simple and symmetrical set of discrete distributions. They also consider the tradeoff between the number of sensors and the communication rate of each sensor when there is a constraint on the total communication rate from the sensors to the fusion center. The results suggest that it is preferable to have several independent sensors transmitting low-rate (coarse) information instead of a few sensors transmitting high-rate (very detailed) information. They also suggest that an M-ary hypothesis testing problem can be viewed as a collection of M(M-1)/2 binary hypothesis testing problems. From this point of view the most useful messages (decision rules) are those that provide information to the fusion center that is relevant to the largest possible numbers of these binary hypothesis testing problems     

Performance Analysis of the Censored Mean-Level Detector

The censored mean-level detector (CMLD) is an alternative to the mean-level detector that achieves robust detection performance in a multiple-target environment by censoring several of the largest samples of the maximum likelihood estimate of the background noise level. Here we derive exact expressions for the probability of detection of the CMLD in a multiple-target environment when a fixed number of Swerling II targets are present. The primary target is modeled by Swerling case II, and only single-pulse processing is analyzed. Optimization of the CMLD parameters is considered, and a comparison to other detectors is presented.     

Performance analysis of linearly combined order statistic CFARdetectors

Linearly combined order statistic (LCOS) constant false-alarm rate (CFAR) detectors are examined for efficient and robust threshold estimation applied to exponentially distributed background observations for improved detection. Two optimization philosophies have been employed to determine the weighting coefficients of the order statistics. The first method optimizes the coefficients to obtain efficient estimates of clutter referred to the censored maximum likelihood (CML) and best linear unbiased (BLU) CFAR detectors. The second optimization involves maximizing the probability of detection under Swerling II targets and is referred to as the most powerful linear (MPL) CFAR detector. The BLU-CFAR detector assumes no knowledge of the target distribution in contrast to the MPL-CFAR detector which requires partial knowledge of the target distribution. The design of these CFAR detectors and the probability of detection performance are mathematically analyzed for background observations having homogeneous and heterogeneous distributions wherein the trade-offs between robustness and detection performance are illustrated     

Detection Performance of Logarithmic Receivers Employing Video Integrators

The detection performance of logarithmic receivers in Rayleigh and non-Gaussian clutter is investigated. In Rayleigh clutter the performance is determined for steady, Swerling case 1, and Swerling case 2 targets. The detection loss of logarithmic receivers is generally less than the ? log n loss conjectured by Green, but consistent with the 1.08-dB asymptotic loss established by Hansen. The Swerling case 2 loss, important in frequency- agility applications, canbe severe for a small number of integrated pulses and high Pd, and apparently approaches the 1.08-dB asymptotic loss as a lower bound. Graphs of GramCharlier series cumulants are provided to allow determination of logarithmic-receiver performance. Curves are presented to allow the detection performance of logarithmic receivers in log-normal and Weibull clutter to be determineds.     

Predetection fusion: resolution cell grid effects

If members of a suite of sensors from which fusion is to be carried out are not colocated, it is unreasonable to assume that they share a common resolution cell grid; this is generally ignored in the data fusion community. We explore the effects of such “noncoincidence”, and we find that what at first seems to be a problem can in fact be exploited. The idea is that a target is known to be confined to an intersection of overlapping resolution cells, and this overlap is generally small. We examine noncoincidence from two viewpoints: tracking and detection. With respect to tracking our analysis is first static, by which is meant that we establish the decrease in measurement error; and then dynamic, meaning that the overall effect in the tracking problem is quantified. The detection viewpoint considers noncoincidence as it has impact on a predetection fusion system. Specifically, the role of the fusion rule is examined, and the use of noncoincidence to improve detection performance (rather than that of tracking) is explored     

Detection and range/Doppler estimation for colocated sensors

The problem of multisensor detection and high resolution signal state estimation using joint maximum a posteriori detection and high order nonlinear filtering techniques is addressed. The model-based fusion approach offers the potential for increased target resolution in range/Doppler/azimuth space. The approach employs joint detection/estimation filters (JDEF) for target detection and localization. The JDEF approach segments the aggregate nonlinear model over the entire target resolution space into a number of localized nonlinear models by partitioning the resolution space into a number of resolution subcells. This partitioning leads to extremely accurate state estimation. The proposed JDEF approach has a built-in capability for automatic data alignment from multiple sensors, and can be used for centralized, decentralized, and distributed data fusion.     

Distributed binary integration

A distributed radar detection system that employs binary integration at each local detector is studied. Local decisions are transmitted to the fusion center where they are combined to yield a global decision. The optimum values of the two thresholds at each local processor are determined so as to maximize the detection probability under a given probability of false alarm constraint. Using an important channel model, performance comparisons are made to determine the integration loss     

A Boolean algebra approach to multiple sensor voting fusion

A technique for integrating multiple-sensor data using a voting fusion process that combines the individual sensor outputs is described. An important attribute of the method is the automatic confirmation of the target by the fusion processor without the need to explicitly determine which sensors and what level of sensor participation are involved. A three-sensor system, with multiple confidence levels in each sensor, is discussed to illustrate the approach. Boolean algebra is used to derive closed-form expressions for the multiple sensor-system detection probability and false-alarm probability. Procedures for relating confidence levels to detection and false alarm probabilities are described through an example. The hardware implementation for the sensor system fusion algorithm is discussed     

KUPS: Knowledge-Based Ubiquitous and Persistent Sensor Networks for Threat Assessment

We propose a knowledge-based ubiquitous and persistent sensor network (KUPS) for threat assessment, in which "sensor" is a broad characterization. It refers to diverse data or information from ubiquitous and persistent sensor sources such as organic sensors and human intelligence sensors. Our KUPS for threat assessment consists of two major steps: situation awareness using fuzzy logic systems (FLSs) and threat parameter estimation using radar sensor networks (RSNs). Our FLSs combine the linguistic knowledge from different intelligent sensors, and our proposed maximum-likelihood (ML) estimation algorithm performs target radar cross section (RCS) parameter estimation. We also show that our ML estimator is unbiased and the variance of parameter estimation matches the Cramer-Rao lower bound (CRLB) if the radar pulses follow the Swerling II model. Simulations further validate our theoretical results.